Problem: Which of the following numbers is a factor of 165? ${5,6,8,9,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $165$ by each of our answer choices. $165 \div 5 = 33$ $165 \div 6 = 27\text{ R }3$ $165 \div 8 = 20\text{ R }5$ $165 \div 9 = 18\text{ R }3$ $165 \div 13 = 12\text{ R }9$ The only answer choice that divides into $165$ with no remainder is $5$ $ 33$ $5$ $165$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $165$ $165 = 3\times5\times11 5 = 5$ Therefore the only factor of $165$ out of our choices is $5$. We can say that $165$ is divisible by $5$.